To visit Katrín Sigurđardóttir's installation Foundation at the Venice Biennale, you must travel to the Palazzo Zenobio in the city's Dorsoduro quarter. There you traverse a courtyard garden, beyond which lies a spacious, grassy yard flanked by walls in diverse masonry. On the far side of the yard is a plain gray building that looks as though it has been sliced through horizontally by the black-and-white-tiled floor of a second, entirely unrelated structure. The plain building is an ex-laundry—a preexisting, if now disused, space—while the floor, which protrudes into the courtyard and on which visitors can walk, is Sigurđardóttir's contribution to this year's Icelandic pavilion, one of the many national pavilions situated within the fabric of the city.

For her ambitious piece, Sigurđardóttir cast thousands of tiles in concrete, inventing a pavement resembling worn marble or travertine in stylized 18th-century ornamental patterns. The floor plan, as well, draws upon elements of 18th-century architecture. In startling contrast, supporting the floor is a substructure of very contemporary-looking particleboard, created by the artist, which is also visible around the pavement's periphery.

Such dislocations are typical of Sigurđardóttir, who toys in her sculpture with slippages of space and time, scale and medium. I met her at Palazzo Zenobio on May 30, just before the opening of the 55th Venice Biennale (through Nov. 24), and we conversed as we walked through and around her striking installation, the floor section of which (not the ex-laundry) will travel in 2014 to the Reykjavik Art Museum and New York's Sculpture Center.

KATRÍN SIGURĐARDÓTTIR It's easiest for me to take as a starting point the work I did at the Metropolitan Museum in New York in 2010. There I made a leap from working primarily with intimate, person-specific memory to collective or cultural memory, as I interacted with the holdings of the museum. Foundation is a continuation of this mining of cultural memory. It is a large surface that maps out an imaginary 18th-century pavilion. It is conceived very two-dimensionally, as a floor plan. I worked for nearly one year just drawing, mathematically composing the pattern.

FAYE HIRSCH There are essentially two facets to your piece—the shape of the floor in relation to the preexisting building, and the pattern in the floor.

SIGURĐARDÓTTIR And of course it's no accident that I chose to create something akin to a pavilion, nor that I chose to create it in an old laundry. The idea was to juxtapose the shell of the laundry with the idea of a pavilion—something made for luxury and leisure. The buildings near the Palazzo are something of a hodgepodge. The laundry also at some point became a boat workshop.

HIRSCH The setting is interesting: you have this big, empty yard and on the other side your installation, which makes the building look like it is in the process of being restored.

SIGURĐARDÓTTIR That wasn't necessarily intentional, though I can see it. Another important aspect of my work is its play with scale—the confusion between what you take in visually and what you take in through a bodily experience.

HIRSCH From the yard, we see what looks like an ordinary door, but don't realize how terribly short it is until we bump our heads when entering the building.

SIGURĐARDÓTTIR Exactly. The door actually continues below the floor—you see only part of the door.

HIRSCH It's a simple device with a complicated effect.

SIGURĐARDÓTTIR Yes.

HIRSCH Did you scout this site?

SIGURĐARDÓTTIR Iceland had this space last time, too. I decided I wanted to use it again, though not until I had scouted a lot of other sites. But I had this idea early on, and it was such a strong idea. The way my work comes to me is very immediate—it just takes root, and I can't go back on it.

It was important to me to leave the site sort of vacant. I wanted nothing in this yard, so you come at the piece, and you take it in not only as a construction, but as part of the entirety of the site, which is such an interesting one. With all these surrounding buildings, there are all these different surfaces, and Foundation is very much about a surface.

HIRSCH Two different surfaces, right? You've consciously contrasted the rough particleboard surface and the concrete tile. And you created that concrete—it is not found material. Did you borrow the pattern from an existing floor, or did you make it up entirely?

SIGURĐARDÓTTIR I studied a lot of ornamental floors from all periods. I wanted to place this floor in the 18th century simply because it was a century of pavilions. But the work is not historical in any way. I looked at 18th-century ornament because it's so much fun.

HIRSCH The black-and-white pattern seems very off somehow. It's not symmetrical.

SIGURĐARDÓTTIR That's exactly right. In some parts of Europe in the 18th century, you often find this Rococo style in ornament that breaks away from the rules.

HIRSCH And you don't join the pattern neatly, which can be a bit dizzying.

SIGURĐARDÓTTIR Part of that has to do with the way the work is constructed. The entire floor is hand-made-we cast something like 9,000 tiles. And they are pigmented concrete—not glazed or fired.

HIRSCH In the black-and-white parts—most of the floor, really—we see a vine motif, a radiating pattern, and some stylized crowns, but at the center is an orange flower resembling a chrysanthemum.

SIGURĐARDÓTTIR Something that I noticed in my research is that the center of these floors is somewhat freehand. It's more like a painting, whereas the rest is a pattern. This was in many ways a very painterly project. I have a background in painting, and in a sense I have never left it completely. Foundation is a very large work, in many senses. I worked on it for a year and a half, and many strands of my work come into it.

HIRSCH The two buildings—the real and imaginary—don't easily mesh. It's not a very sympathetic relationship.

SIGURĐARDÓTTIR They don't fit—but somehow they do, in the sense that you are actually standing on the floor of the "pavilion," and you are looking at the ceiling of the laundry. But they don't fit, in terms of the design.

HIRSCH You've given the edges of the floor a very intricate shape. One imagines that it would have been the floor of a very fancy room, which the laundry is not at all.

SIGURĐARDÓTTIR It's a meeting of the ornamental and the austere. I based the floor plan on designs of rooms mostly in Italy, but it's the type of space you would find all over Europe. Of course, the floor is made in a way that never existed, ever. It's a parquet pattern, yet it's made with tiles, and the tiles are not marble or travertine, but concrete.

HIRSCH Did you imagine the entire elevation of the room?

SIGURĐARDÓTTIR Yes. And I made about four site visits here when I was drawing the piece, and during that time I positioned and sized the sculpture to create an interesting space.

HIRSCH From upstairs looking down, you can really see that it's a sculpture and not architecture.

SIGURĐARDÓTTIR Exactly. This is just one of the things that I realized when I encountered this building. Here was the chance to make a very large drawing [in space] that could be experienced either as a drawing or a sculpture. You cannot take in the entirety of the work from one viewpoint, so in that sense it is huge. Only by moving through the site can you experience it as a whole.

HIRSCH It's interesting how you break the continuity of the radiating tile pattern. You feel that the floor was not one floor, but many, that you somehow excerpted.

SIGURĐARDÓTTIR There was one particular pattern I studied that had this peculiar combination of floral and geometric patterns. You see in 18th-century floor designs these Op-ish patterns but also some Orientalizing motifs.

HIRSCH Could you speak a bit about the combination of the particleboard and the tiling?

SIGURĐARDÓTTIR In scenography, you have painted landscape, and on the backside you see something that looks like the underside of my sculpture. In a sense, this contrast between the two surfaces is very consistent in my work. My sculpture always has a two-sidedness. I'm often drawing out these illusionistic spaces, yet at the same time as I create them, I kill them.

Whenever I start a new work, I'm always answering a question that I raised in the previous work. At the Met, I chose to copy and work from boiseries that were in the collection. It's such an interesting process, to extract a decorative surface from its original place, install it somewhere else—say, in a private residence in another city and another country—where you can think of yourself as somehow being in the place where it was originally. The work migrates, and the visitor continues to have an experience of a place that is far away in space and time. So this floor is very much a continuation of that inquiry. Showing this very contemporary material—the particleboard—is a way to insert a footnote in the experience of the work. It tells us that we are in fact in the here-and-now. We're being fooled-in the way that painting both fools you and tells the truth.

HIRSCH You are Icelandic, and you have lived in the United States for quite a long time. So you are in a sense a displaced person. Is there any of that in the work?

SIGURĐARDÓTTIR Surely.

HIRSCH And here we are in the Icelandic pavilion, which is not in the Giardini.

SIGURĐARDÓTTIR Part of the intention of the work is to take the idea of the pavilion all the way. I mean, anything can be a pavilion!

HIRSCH The original idea of a pavilion was to create a structure that could be disassembled and, perhaps, moved.

SIGURĐARDÓTTIR It was a place of leisure or sport in proximity to a palace. There were all these themed pavilions in the 18th century.

HIRSCH How are you going to adapt this piece for the Reykjavik Art Museum and the Sculpture Center in New York, when it seems so specific to this site?

SIGURĐARDÓTTIR The ornamental floor is going to be removed. In Reykjavik you will have a void in the form of the building in Venice, and in New York you will have a void of the building in Venice and the building in Reykjavik. The floor is a suggestive remnant of another time. The true voids that remain are going to become more visible as the work travels. I think what is going to happen is that the experience of the work, and the work's meaning, are really going to transform. That's what I hope.

The Icelandic Pavilion was organized by Sculpture Center director Mary Ceruti along with Ilaria Bonacossa, curator of exhibitions at Genoa's Museum of Contemporary Art Villa Croce.

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